The use of competing risk frameworks for the analysis of reliability/survival data has gained popularity in recent years, primarily because traditional techniques are inadequate for effectively analyzing such data. In this study, we examined the independent competing risks model with lifetimes of units distributed according to the Nadarajah–Haghighi distribution. Our focus was on estimating the unknown parameters, as well as the reliability and failure rate functions, using both frequentist and Bayesian estimation methods under an improved adaptive progressive Type-Ⅱ censoring mechanism. The frequentist estimation involved deriving point estimators and approximate confidence intervals using the asymptotic properties of classical estimators. Bayes estimators were obtained through symmetric squared loss and the Metropolis-Hastings algorithm, which generated samples from the joint posterior distribution. Additionally, the highest posterior density credible intervals were calculated. Given the complex nature of the acquired estimators, we conducted a comprehensive simulation study to numerically compare the performance of the proposed estimates across various experimental scenarios. To empirically validate the proposed inferential framework, we analyzed two real-world competing risk datasets, highlighting the effectiveness of the applied techniques in reliability data analysis.